@Article{Cho2016,
author = "Cho, Ilwoo",
title = "Certain group dynamical systems induced by Hecke algebras",
journal = "Opuscula Math.",
year = "2016",
volume = "36",
number = "3",
pages = "337--373",
doi = "http://dx.doi.org/10.7494/OpMath.2016.36.3.337",
url = "http://dx.doi.org/10.7494/OpMath.2016.36.3.337",
abstract = "In this paper, we study dynamical systems induced by a certain group \(\mathfrak{T}_{N}^{K}\) embedded in the Hecke algebra \(\mathcal{H}(G_{p})\) induced by the generalized linear group \(G_{p} = GL_{2}(\mathbb{Q}_{p})\) over the \(p\)-adic number fields \(\mathbb{Q}_{p}\) for a fixed prime \(p\). We study fundamental properties of such dynamical systems and the corresponding crossed product algebras in terms of free probability on the Hecke algebra \(\mathcal{H}(G_{p})\).",
keywords = "free probability, free moments, free cumulants, Hecke algebra, normal Hecke subalgebra, free probability spaces, representations, operators, Hilbert spaces, dynamical systems, crossed product algebras",
issn = "1232-9274"
}